An amenability property of algebras of functions on semidirect products of semigroups

Abstract

Let S1 and S2 be semitopological semigroups, S1 τ  S2 a semidirect product. An amenability property is established for algebras of functions on S1 τ  S2. This result is used to decompose the kernel of the weakly almost periodic compactification of S1 τ  S2 into a semidirect product.